A338693 a(n) = Sum_{d|n} d^(d - n/d) * binomial(d, n/d).

1, 4, 27, 257, 3125, 46665, 823543, 16777312, 387420490, 10000001250, 285311670611, 8916100467712, 302875106592253, 11112006825910963, 437893890380859625, 18446744073716891649, 827240261886336764177, 39346408075296709766628, 1978419655660313589123979

Offset

1,2

Links

Winston de Greef, Table of n, a(n) for n = 1..385

Formula

G.f.: Sum_{k>=1} ( (k + x^k)^k - k^k ).

If p is prime, a(p) = p^p.

Mathematica

a[n_] := DivisorSum[n, #^(# - n/#) * Binomial[#, n/#] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(d-n/d)* binomial(d, n/d));
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k+x^k)^k-k^k))

Crossrefs

Cf. A318636, A318637, A318638, A338685, A338694.

Sequence in context: A050764 A302108 A240582 * A360776 A360728 A353014

Adjacent sequences: A338690 A338691 A338692 * A338694 A338695 A338696

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2021

Status

approved